{"paper":{"title":"Invariant varieties of periodic points for some higher dimensional integrable maps","license":"","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Noriko Saitoh, Satoru Saito","submitted_at":"2006-10-25T19:49:44Z","abstract_excerpt":"By studying various rational integrable maps on $\\mathbf{\\hat C}^d$ with $p$ invariants, we show that periodic points form an invariant variety of dimension $\\ge p$ for each period, in contrast to the case of nonintegrable maps in which they are isolated. We prove the theorem: {\\it `If there is an invariant variety of periodic points of some period, there is no set of isolated periodic points of other period in the map.'}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0610069","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}